Uncertainty and compound lotteries: Calibration

This paper introduces a theoretical model of decision making in which preferences aredefined on both Savage subjective acts and compound objective lotteries. Preferencesare two-stage probabilistically sophisticated when the ranking of acts correspondsto the ranking of the respective compound lotteries induced by the acts throughthe decision maker’s subjective belief. This family of preferences includes varioustheoretical models proposed in the literature to accommodate non-neutral attitudetowards ambiguity. The principle of calibration relates preferences over acts and com-pound objective lotteries, and provides a foundation for the tight empirical associationbetween probabilistic sophistication and reduction of compound lotteries for all two-stage probabilistically sophisticated preferences